scholarly journals On the Nordtvedt effect in Minkowski spacetime with nonlinear connection

2017 ◽  
Vol 6 (4) ◽  
pp. 130
Author(s):  
Kostadin Trenčevski ◽  
Emilija Celakoska
Keyword(s):  
Minkowski Space ◽  
Minkowski Spacetime ◽  
Gravitational Theory ◽  
Chemical Compositions ◽  
Lunar Laser Ranging ◽  
Nonlinear Connection ◽  
The Earth ◽  
Gravitational Theories ◽  
Lunar Laser ◽  
The Mathematical Model

The Lunar Laser Ranging (LLR) experiment provided precise data which brought the possibility to make more stringent conclusions for the foundations of gravitational theories, i.e. the Equivalence Principles. Beside some effects of non - gravitational origin, the LLR data was fitted with the well-known gravitational effects such as the apsidal and geodetic precessions, the time delay, etc. The Nordtvedt effect in General Relativity (GR) vanishes, while the LLR experiment data of the Earth-Moon distance and the laboratory experiments with experimental bodies made of different chemical compositions measured a variation of distance in millimeters. According to the mathematical model of gravitation in Minkowski space endowed with a nonlinear connection we obtained a result closer to the experimental measurements. More precisely, we obtained a difference of 0.17 mm (or 0.28 mm, depending on the value of the scaling factor) from the LLR measurements of the variation of the Earth-Moon distance, while the corresponding result in GR makes a difference from the LLR measurements of 5.7 mm. The gravitational theory with nonlinear connection in Minkowski space gives the same results for the confirmed GR effects, nevertheless it yields some additional variations of the distance concerning the Nordtvedt effect.

Effect of non-tidal station loading on Lunar Laser Ranging observatories and on the estimation of Earth orientation parameters

2021 ◽  
Author(s):  
Vishwa Vijay Singh ◽  
Liliane Biskupek ◽  
Jürgen Müller ◽  
Mingyue Zhang
Keyword(s):  
Research Centre ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Earth Orientation Parameters ◽  
Tidal Station ◽  
Earth Orientation ◽  
The Earth ◽  
Lunar Laser ◽  
Orientation Parameters

<p>The distance between the observatories on Earth and the retro-reflectors on the Moon has been regularly observed by the Lunar Laser Ranging (LLR) experiment since 1970. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon, and a higher number of LLR observations in total. Providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics, LLR can also support the estimation of Earth orientation parameters (EOP), like UT1. The increased number of highly accurate LLR observations enables a more accurate estimation of the EOP. In this study, we add the effect of non-tidal station loading (NTSL) in the analysis of the LLR data, and determine post-fit residuals and EOP. The non-tidal loading datasets provided by the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS), and the EOST loading service of University of Strasbourg in France are included as corrections to the coordinates of the LLR observatories, in addition to the standard corrections suggested by the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions. The Earth surface deforms up to the centimetre level due to the effect of NTSL. By considering this effect in the Institute of Geodesy (IfE) LLR model (called ‘LUNAR’), we obtain a change in the uncertainties of the estimated station coordinates resulting in an up to 1% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%. In a second part of the study, we investigate whether the modelling of NTSL leads to an improvement in the determination of EOP from LLR data. Recent results will be presented.</p>

scholarly journals Relativistic rotational effects: application to the Earth-Moon system

1996 ◽  
Vol 172 ◽  
pp. 321-324 ◽  
Author(s):  
David Vokrouhlický
Keyword(s):  
Coordinate System ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Moon System ◽  
Geodetic Precession ◽  
Spin Effects ◽  
The Earth ◽  
Relativistic Spin ◽  
Lunar Laser

Relativistic spin effects involved in the Earth-Moon dynamics are reviewed. They enclose: (i) the coordinate system effects, and (ii) the relativistic physical librations. The geodetic precession is the only relativistic spin phenomenon which has been firmly detected so far. The best candidates of the effects which might be detected in the forthcoming period are the lunar physical librations and coordinate nutations. As for the latter, however, a fine cancellation between the geodetic and the Lense-Thirring coordinate effects results in decreasing their amplitude just below the possibility of the Lunar Laser Ranging technology.

scholarly journals Relations Between Celestial and Selenocentric Reference Frames

1981 ◽  
Vol 63 ◽  
pp. 268-280
Author(s):  
J. Kovalevsky
Keyword(s):  
Reference Frames ◽  
Center Of Mass ◽  
Great Accuracy ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Geometric Means ◽  
The Earth ◽  
Lunar Laser ◽  
Unique System ◽  
Different Types

AbstractThe very great accuracy with which the motions of the Moon can now be monitored by laser ranging, differential VLBI and occultation observations, implies that the interpretation of the measurements is conditioned by the choice and the accurate knowledge of a selenocentric, a terrestrial and a celestial frames. Two different types of selenocentric reference frames can be envisioned. The present selenographic frames are discussed but the author proposes that one should introduce a system defined by a purely geometric means. Some consequences of such a choice are discussed. One feature of the future conventional terrestrial frame is very important for Earth-Moon dynamics. Its origin should coincide with the center of mass of the Earth as determined by lunar laser ranging. As far as the quasi-inertial reference systems are concerned, the liaisons between a purely lunar dynamical system, subject to some hardly modelable effects, and purely celestial systems are analysed. The reduction of observations made with various techniques implies the use of different systems, and several problems are stated that should be solved before a unique system for Earth-Moon dynamics might be used.

scholarly journals Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser Ranging

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Yi Xie ◽  
Sergei Kopeikin
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Reference Frames ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Local Frame ◽  
The Earth ◽  
Lunar Laser ◽  
Lunar Motion ◽  
New Generation

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser RangingWe overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, β and γ, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames - geocentric (GRF) and selenocentric (SRF) - have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable quantities such as the proper time and the round-trip laser-light distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the post-Newtonian multipole moments of the gravitational field of Earth and Moon. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom.

scholarly journals MILLIMETRE MOON MEASUREMENT: 50 YEARS OF LUNAR LASER RANGING SINCE APOLLO 11!

2020 ◽  
Vol XLIII-B3-2020 ◽  
pp. 1105-1110
Author(s):  
J. F. Brock
Keyword(s):  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Space Race ◽  
Lunar Laser ◽  
Space Star ◽  
Gravitational Influence ◽  
Tv Shows ◽  
Set Up

Abstract. Since the dawn of time the Moon has held fascination for the earliest humans who saw it as a natural navigational beacon, a heavenly body to be revered and a poetic inspiration. Ancient art features the Moon as a prominent subject from all epochs and genres. The name “lunatic” infers that it drives men insane. Giant tides and rapid recessions of water are all attributed to its gravitational influence. As a young boy I was thrilled by stories of Moon travel like Jules Verne’s “From the Earth to the Moon” plus TV shows and movies such as “Lost in Space”, “Star Trek” and “Dr. Who.”The Russian-American “Space Race” focussed on the exciting possibility of man landing on the Moon. I cannot forget the live telecast of the Apollo 11 astronauts on the Moon’s surface in 1969 when I was 13 years old. Four years later I decided to be a land boundary surveyor trained in precise measurement for land title creation. My curiosity was alerted to the Apollo 11 laser ranging aspect of the project when the US team set up a bank of retro-reflectors for measurements from powerful devices on the Earth in the same way we Earthly surveyors make our daily measurements using such EDM equipment.In this paper I will describe the techniques and equipment utilised during this accurate Moon positioning project. You will also see the Earth observatories still measuring to five sites on the Moon and some ancient admirable attempts to determine this distance.

scholarly journals LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON

2009 ◽  
Vol 18 (07) ◽  
pp. 1129-1175 ◽  
Author(s):  
JAMES G. WILLIAMS ◽  
SLAVA G. TURYSHEV ◽  
DALE H. BOGGS
Keyword(s):  
Equivalence Principle ◽  
Primary Objective ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Wide Range ◽  
Near Term ◽  
Ppn Parameters

A primary objective of the lunar laser ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of the highly accurate measurements of the distance between the Earth and the Moon provide unique information used to determine whether, in accordance with the equivalence principle (EP), these two celestial bodies are falling toward the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Thirty-five years since their initiation, analyses of precision laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-1.0 ± 1.4) × 10-13 for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, Δ(MG/MI). This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of Δ(MG/MI) SEP = (-2.0 ± 2.0) × 10-13. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter η of (4.4 ± 4.5) × 10-4, where η = 4β - γ - 3 and both γ and β are parametrized post-Newtonian (PPN) parameters. Using the recent result for the parameter γ derived from the radiometric tracking data from the Cassini mission, the PPN parameter β (quantifying the nonlinearity of gravitational superposition) is determined to be β - 1 = (1.2 ± 1.1) × 10-4. We also present the history of the LLR effort and describe the technique that is being used. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR accuracy will further advance the research on relativistic gravity in the solar system and, most notably, will continue to provide highly accurate tests of the EP.

scholarly journals Agreements and Disagreements between Theories of Rigid Earth Nutation

1997 ◽  
Vol 165 ◽  
pp. 319-324
Author(s):  
J. Souchay
Keyword(s):  
Very Long Baseline Interferometry ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Theoretical Determination ◽  
Long Baseline ◽  
The Earth ◽  
Lunar Laser ◽  
Rigid Earth ◽  
Good Agreement

AbstractThe necessity to elaborate a theory of nutation and precession matching the accuracy of very modern techniques as Very Long Baseline Interferometry and Lunar Laser Ranging led recently to various works. We discuss here the good agreement between those related to the nutation when considering the Earth as a solid body. In comparison we show the uncertainty concerning the modelisation of the transfer function leading to theoretical determination of the nutation coefficients when including dominant geophysical characteristics.

Equivalence principle for massive bodies in a generalized theory of gravitation. II

1982 ◽  
Vol 60 (11) ◽  
pp. 1556-1560 ◽  
Author(s):  
J. C. McDow ◽  
J. W. Moffat
Keyword(s):  
Equivalence Principle ◽  
Equations Of Motion ◽  
Upper Bounds ◽  
Laser Ranging ◽  
Coordinate Frame ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Theory Of Gravitation ◽  
Three Body

The three-body equations of motion are examined for periodic perturbations in an earth centered coordinate frame. The lunar-laser-ranging data is then used to place upper bounds on the new l parameters associated with the earth and sun.

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